What is the formula for gravity loss on a rocket launch and how was it derived?

In summary, the conversation discusses the formula for gravity loss on a rocket launch, which takes into account the gravitational acceleration and flight path angle. The formula is derived by integrating the component of the gravitational force along the velocity of the rocket over the entire flight time. It is also mentioned that acceleration orthogonal to the direction of motion does not affect the speed.
  • #1
Januz Johansen
34
1
Hello all!
Lately i have been looking at many rocket equations, and i was wondering about the gravity loss on a rocket launch. I found the formula for the gravity loss
upload_2016-12-2_21-16-52.png

where g is of course the gravitational acceleration, and y is the flight path angle, but can somone explane why it looks like this? How has this been deduced?
Thanks
 
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  • #2
It is the component of the gravitational force along the velocity of the rocket (=the component changing the velocity), integrated over the whole rocket flight time.
 
  • #3
mfb said:
It is the component of the gravitational force along the velocity of the rocket (=the component changing the velocity), integrated over the whole rocket flight time.

Okay thanks
But why do we have to take the Angle into accound?
 
  • #4
Acceleration orthogonal to the direction of motion does not change the speed.
 
  • #5
mfb said:
Acceleration orthogonal to the direction of motion does not change the speed.
Okay thank you
 

Related to What is the formula for gravity loss on a rocket launch and how was it derived?

What is gravity loss of a rocket?

Gravity loss of a rocket is the decrease in velocity and potential energy of a rocket as it travels through the Earth's gravitational field. This is due to the force of gravity acting on the rocket and causing it to lose energy.

How does gravity loss affect a rocket's trajectory?

Gravity loss can significantly affect a rocket's trajectory by reducing its speed and altering its path. This can result in a lower altitude and shorter distance traveled compared to a rocket that does not experience gravity loss.

Can gravity loss be avoided?

Gravity loss cannot be completely avoided, as it is an inherent consequence of launching a rocket from Earth. However, engineers and scientists can minimize its effects by carefully designing the rocket's trajectory and using more efficient propulsion systems.

How does the mass of a rocket affect gravity loss?

The mass of a rocket does not directly affect gravity loss, as the force of gravity is dependent on the mass of the Earth, not the rocket. However, a heavier rocket will require more fuel to overcome the force of gravity, leading to a higher amount of gravity loss.

Why is gravity loss important to consider in rocket design?

Gravity loss is an important factor to consider in rocket design because it can significantly impact the rocket's performance and efficiency. By minimizing gravity loss, engineers can optimize the rocket's trajectory and ultimately increase its payload capacity and potential distance traveled.

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